The role of the plasmon in interfacial charge transfer

The lack of a detailed mechanistic understanding for plasmon-mediated charge transfer at metal-semiconductor interfaces severely limits the design of efficient photovoltaic and photocatalytic devices. A major remaining question is the relative contribution from indirect transfer of hot electrons generated by plasmon decay in the metal to the semiconductor compared to direct metal-to-semiconductor interfacial charge transfer. Here, we demonstrate an overall electron transfer efficiency of 44 ± 3% from gold nanorods to titanium oxide shells when excited on resonance. We prove that half of it originates from direct interfacial charge transfer mediated specifically by exciting the plasmon. We are able to distinguish between direct and indirect pathways through multimodal frequency-resolved approach measuring the homogeneous plasmon linewidth by single-particle scattering spectroscopy and time-resolved transient absorption spectroscopy with variable pump wavelengths. Our results signify that the direct plasmon-induced charge transfer pathway is a promising way to improve hot carrier extraction efficiency by circumventing metal intrinsic decay that results mainly in nonspecific heating.

. The bulk damping contribution to the linewidth is represented by the grey area in Fig. 2C.Grad was accounted for according to Grad = ℎ/, where ℎ is Planck's constant and a proportionality constant of  = 3.34 × 10 23 fs -1 nm -3 was used based on previous results for gold nanorods (AuNRs) of similar size on a quartz substrate (55).The volume, , was extracted for each individual AuNR by correlated scanning electron microscopy (81).GCID was then obtained by subtracting GBulk and Grad from the measured linewidth, G, for all individual nanoparticles, while the CID efficiency ηCID, signifying the direct charge transfer efficiency ηDirect, was calculated as the ratio between GCID and G.We note that plasmon damping due to electron-surface scattering is small enough to be neglected for the dimensions of the AuNRs (26 ± 2 × 49 ± 3 nm) studied here (55).
This approach does not consider that Grad is expected to also have a resonance energy dependence.Following the method described in Ref. (82) we estimate this effect to be on the order of ~5 meV causing a reduction in charge transfer efficiency by 4%, which is on the order of the error for these measurements.In addition, this resonance energy dependence assumes that the nonradiative damping processes are unchanged, i.e. no CID.We therefore decided to neglect this potential additional linewidth contribution, but acknowledge that more detailed studies are needed on systems that show only resonance energy dependent radiation damping compared to those that also support CID.

Charge transfer efficiencies from IR/NIR transient absorption spectroscopy
The total charge transfer efficiencies (direct + indirect pathways) followed by IR/NIR transient absorption of the electrons injected into the TiO2 conduction band were obtained from fluencedependent measurement of the signal amplitude for gold nanorod@TiO2 core-shell heterostructures (AuNRs@TiO2) compared to direct bandgap excitation for TiO2 control samples.This analysis assumes that the initial signal at zero pump-probe delay times, DAmax, is proportional to the free carrier concentration and scales linearly with the absorbed photon density for TiO2.We accounted for the absorbed photon density based on n +. = ( +"4+ ) •  /ℏ +"4+ (13).Here  +"4+ is the pump photon energy and  is the pump fluence.The pump beam diameter was 210 μm at the sample.( +"4+ ) is the absorption determined at the pump energy for ech sample according to Fig. S2.In Fig. 3E, the error in absorbed photon densities was calculated by propagating the uncertainties derived from the measurements of pump fluence and beam diameter.The same linearity of DAmax with absorbed photon density was also observed for the AuNRs@TiO2, but the slope was smaller (Fig. 3E), consistent with a less than 100% charge injection efficiency.The ratio of slopes between AuNR@TiO2 and TiO2 samples yielded the calculated total charge transfer efficiencies.This analysis, however, neglects that for different excitation wavelengths the electrons injected into the TiO2 conduction band might have different initial energies, leading to different absorption cross sections, as reported previously for charge injection from ruthenium and rhenium dyes (83).While we cannot exclude this possibility, we note that the excellent agreement between the wavelength dependent total charge transfer efficiencies found for probing in the IR/NIR vs. the visible regions (Fig. 5A) suggests that it only plays a minor role for the system studied here.Furthermore, the charge transfer efficiency of 44% at the main plasmon resonance for the AuNRs@TiO2 agrees well with a value of 20-50% measured for 2-10 nm silver nanospheres on TiO2 (19) and 25-45% measured for 10 nm gold nanospheres (13,17), when similarly exciting on resonance and using IR transient absorption spectroscopy.

Charge transfer efficiencies from visible transient absorption spectroscopy
The transient bleach recovery dynamics probed at the visible plasmon resonance are proportional to the electronic temperature (71,84).Interfacial charge transfer lowers the electronic temperature in the AuNR@TiO2 heterostructures.Taking the ratio of the slopes for the fluencedependent measurements of the bleach recovery dynamics for AuNRs@TiO2 compared to AuNRs then yields the charge transfer efficiency (13).The bleach recovery dynamics were extracted from the data based on the two-temperature model that has been widely used for metals to model the relaxation dynamics of excited electrons by coupling to a phonon bath through electron-phonon interactions (2,3,(12)(13)85).The electron distribution relaxes from an initial nonthermal (NT) to a thermalized (Th) distribution through electron-electron scattering.The temporal evolution of the electron and phonon temperatures upon ultrashort pulse excitation is given by (68,69): C e (T e ) dT e dt =-g(T e -T l ) and C l dT l dt =g(T e -T l ), where, C e =γT e is the temperaturedependent electronic heat capacity, which has a linear relationship with the temperature in the low-temperature regime (< ~3000 K for Au) (67,86).g is the electron heat capacity constant (66 Jm -3 K -2 for Au).C l represents the lattice heat capacity (68,87).g denotes the electron-phonon coupling constant.T e and T l are the electronic and lattice temperatures, respectively.We employed this two-temperature model to quantify the plasmon bleach dynamics expressed as the differential transient transmission ∆  ⁄ (ℎ, ) according to (40,84): defines the thermalization time of electrons.The temperature of the thermalized electron distribution decreases due to electron-phonon interactions with a time of  (2+. .By fitting of the data to this model, we obtained  (2+.as a function of pump fluence at different excitation wavelengths for the AuNR@TiO2 heterostructures and AuNR controls. It needs to be stressed though that the linearity of  (2+. is with respect to T e , which in turn depends on the square root of the total energy absorbed from the pump beam determined by the nanoparticle absorption crosse section and the incident fluence (71).However, for the range of pump fluences used here, an approximate linear dependence between  (2+.and absorbed fluence holds, as seen in Figs.4C and S6.Furthermore, plotting  (2+.against incident instead of absorbed fluence is justified here because we adjusted the optical densities of the AuNR@TiO2 and AuNR films to be the same with respect to the contribution from the Au (see Figs. 2G-2I, i.e. difference between 2G and 2H compared to 2I).Because of the broad surface plasmon resonance (SPR) of the films this approach is furthermore justified for the different excitation wavelengths.

Transmission electron microscopy of AuNRs@TiO2
The AuNR@TiO2 samples were prepared for transmission electron microscopy by drop-casting an appropriate concentration of the solution onto 5 nm thick SiN window grids (SN100H-A05Q33A, SiMPore).Samples were imaged after subjecting them to the same thermal annealing conditions as described in the main text, following their deposition on the grids.Transmission electron microscopy was performed using a FEI Titan ETEM operated at a 300 kV acceleration voltage.Images were captured using a Gatan OneView and K3 camera.Selected area electron diffraction was performed using a 10 µm aperture to select < 10 nanorods for a single diffraction pattern.Diffraction simulation analysis was performed using the SingleCrystal software package and reference library.Selected area electron diffraction images were converted into .tiffiles and imported to SingleCrystal.The Au <111> diffraction peaks were used to calibrate the image dimensions within SingleCrystal.Then the simulated powder diffraction pattern was overlaid for Au and rutile and anatase TiO2 revealing good agreement for anatase, which has superior charge injection properties (88).Fourier transforms were computed using the full frame images in Figs.S1B and S1F within Gatan Micro Studio.These images were then filtered by selecting the pixels with intensity greater than the mode.

Atomic force microscopy of TiO2
The surface topography of the TiO2 samples was also characterized by atomic force microscopy.We found a thickness of 500 nm with a roughness of 100 nm for the TiO2 nanoparticle film.For these measurements, we used a Park AFM NX20 under ambient conditions.All imaging was acquired in tapping mode using silicon-tip on nitride lever probes (ScanAsyst, f0 = 70 kHz, Bruker) with a reflective aluminum coating.Atomic force microscopy images were acquired with 256 × 256 pixels and a 0.3 Hz cantilever-tip scan rate.Image analysis was performed using the NanoScope analysis software (version 1.5).

Persson CID model
In this work we used a model proposed by Persson to quantitatively describe the influence of the chemical environment on the SPR of metal particles (36).Here we provide a simplified description of this theory, adopting the same terminology and symbolic notations used by Persson in the original publication (36).
In this model the width (full width at half maximum, FWHM)  of the SPR is given by,  = >?' @ (S.1) where  A is the Fermi velocity for a spherical particle with radius R embedded in a matrix, and C represents the proportionality constant of contributions from diffusive scattering of the electrons at the particle surface and depends on the particle radius (89).The tangential and normal components of the adsorbate induced surface electric field gives two contributions to , denoted as  ∥ and  C , respectively.The tangential component  ∥ is given by, where  E is the number of adsorbates per unit surface area and  FGHH is the cross section for diffusive electron scattering evaluated at the SPR frequency Ω and is given by, where  A is the Fermi frequency, n is the carrier concentration, and Q is a number that depends on the symmetry of the resonance state with Q = 0.2 for s or pz symmetry and Q = 0.3 for px, py symmetry of the adsorbate orbitals.The function  FGHH depends on the nature of the chemical bond between the adsorbate molecules and the particle substrate.The integral (Ω) is given by, where the projected density of states  E () is given by, and  E is the position of the adsorbate induced resonance or virtual state with width (FWHM) Λ (see Fig. 5 of main text and Fig. 2 of Ref. (36)) and  A = ℏ A is the Fermi energy.The evaluation of (Ω) at the observed position of the SPR (Ω) and inserting the obtained value of  FGHH in Eq. (S.2) gives the tangential component of the adsorbate induced contribution to the SPR width.The normal component  C is given by, where  I is the bulk dielectric constant and  is the polarizability of the adsorbate.The integral Im  C is given by, (S.7) where e is the elementary charge and d is the separation of the dynamic image plane and the center of the adsorbate orbital.The evaluation of Im  C (Ω) at the observed position of the SPR (Ω) by using Eq.(S.7) and inserting the obtained value in Eq. (S.6) gives the normal component of the adsorbate induced contribution to the SPR width.
To calculate the extent of CID for AuNRs@TiO2 with the Persson model, we used  A = 5.53 eV,  A =1.40×10 16 Å/s, and n = 0.059 Å -3 for Au (90).With Q = 0.3 for px and py orbital symmetry of TiO2 and introducing an extra factor of two to account for both of the 2π* resonance states in Eq. (S.3), we obtained  I =41.4 Å 2 .To find the value of  E we used the sum of the Au-TiO2 Schottky barrier and one half of Λ of the TiO2 induced virtual/resonance state.The Schottky barrier is defined as the energy difference between the valence (or conduction) band edge of the semiconductor and the Fermi energy of the metal (91).However, in the Persson model,  E is the center of the adsorbate induced resonance state and not its edge.The sum of one half of the width Λ and the Schottky barrier therefore gives the correct value for  E .Using a Schottky barrier of 1.25 eV (54) and Λ = 0.8 eV for the TiO2 induced virtual/resonance state centered at  E −  A =1.65 eV, Eq. (S.4) was used to evaluate the integral () (Fig. S7).The value of (Ω) at the observed position of the SPR (Ω=1.82 eV) was calculated to be 0.19 eV.
The Persson model assumes that the metallic particles are spherical objects with radius R. The AuNR@TiO2 hybrids were rod shaped though with core dimensions of 26 ± 2 × 49 ± 3 nm.We therefore calculated the electron mean free path of the AuNR core by using the geometrical probability approach given by Coronado and Schatz (80) and then determined the radius of a sphere with the same mean free path.According to this approach, the effective mean free path  UHH of a prolate cylinders is  UHH = 2/( + 2) with  the diameter and  the height of the cylinder, yielding an aspect ratio  = /.For the AuNR@TiO2 sample, we hence employed  = 26 ± 2 nm, D = 49 ± 3 nm, r = 0.53 ± 0.07 nm and  UHH = 20.5 ± 1.5 nm.To calculate the radius R of an equivalent sphere with  UHH = 20.5 nm, we used  UHH = (4/3), (80), giving R = 15.4 ± 1.1 nm.Inserting this value for R,  VWXX (Eq.(S.3)), and the number of TiO2 resonance states per unit surface area, na = 0.1 Å -2 (36) in Eq. (S.2), we obtained  ∥ =18 ± 1 meV.
To calculate the normal component  C , we used the separation of the dynamic image plane and the center of the TiO2 orbital,  =  , − ( P /2) = 0.966 Å where D1 = 2.04 Å is the distance between mean planes of two Au layers in the crystal structure of Au (92) and D2 = 1.98 Å is the distance between the mean plane of the outer Au layer and the TiO2 layer (93).Inserting the elementary charge e = 3.794 eV 1/2 Å 1/2 and accounting for both 2π* orbitals of TiO2, Im  C () at the observed position of the SPR (Ω) was calculated from Eq. (S.7) and is shown in Fig. S8.Inserting the value of Im  C () and the dielectric constant of TiO2 ( 94), e0 = 60, in Eq. (S.6), we obtained  C = 1 ± 0.1 meV.The total width due to CID, Hypothetical systems in which the broadening arises from isolated defect sites at the surface were also considered.This calculation was achieved by varying both the resonance state energy,  E , and the adsorbate concentration, na, leaving the rest of the parameters as described above.The results are summarized in Table S1.The total broadening in these cases is far below the experimentally observed broadening, indicating that the broadening arises from states inherent to the interface itself, rather than from isolated defect sites.
Open source software to evaluate the integrals J(w) and Im  C (), and hence to calculate  ∥ and  C may be downloaded at: https://zenodo.org/doi/10.5281/zenodo.11243156We ask that future users of this tool cite the present paper.

Additional resource for Persson model
Additional open-source software that is subject to future development may be downloaded at: https://github.com/blevine37/ChemDampPerssonFig. S1.High resolution transmission electron microscopy of AuNR@TiO2 hybrids before (A-C) and after thermal annealing (E-G).The unannealed particles exhibited an amorphous TiO2 shell while the crystalline Au core is apparent (C, D).After thermal annealing, the TiO2 shell showed domains of crystalline TiO2.Thermal annealing also slightly reshaped the AuNR core, but overall nanorod geometry was maintained.Although the crystallinity of the core was obfuscated by the crystal lattice of the TiO2 (G, H), we did not expect a change for Au.We determined that the TiO2 was in the anatase crystal structure by fitting the diffraction rings in the selected area diffraction pattern to Au (I), anatase (J), and rutile (K) diffraction patterns and found excellent agreement with Au and anatase, but not with rutile.and (G-I) absorption of films made from AuNRs@TiO2 (blue), TiO2 (black), and AuNRs (red).It is possible that the reported charge carrier injection efficiency at 400 nm was overestimated if TiO2 can be directly excited.This issue could be a concern especially because the absorption properties of TiO2 can exhibit variations based on its crystallinity.However, The TiO2 used here has almost negligible absorption beyond 400 nm (Fig. S2H), different from Ref. (19).It is therefore necessary to always emphasize the importance of material-specific characterization due to such variability in absorption characteristics (88).

Fig. S2 .
Fig. S2.(A-C) Transmission, (D-F) reflection, and (G-I) absorption of films made fromAuNRs@TiO2 (blue), TiO2 (black), and AuNRs (red).It is possible that the reported charge carrier injection efficiency at 400 nm was overestimated if TiO2 can be directly excited.This issue could be a concern especially because the absorption properties of TiO2 can exhibit variations based on its crystallinity.However, The TiO2 used here has almost negligible absorption beyond 400 nm (Fig.S2H), different from Ref.(19).It is therefore necessary to always emphasize the importance of material-specific characterization due to such variability in absorption characteristics(88).

Fig. S3 .
Fig. S3.Ultrafast rise and decay of AuNR@TiO2 heterostructures probed at 5 μm upon 515 nm excitation (green line).The black dashed line shows the fit to the experimental data, exhibiting an instrument-limited rise time of ~200 fs.

Fig. S4 .
Fig. S4.(A) Fluence-dependent IR transient absorption pump-probe spectroscopy of AuNR@TiO2 heterostructures.Ultrafast dynamics of AuNR@TiO2 heterostructures were probed at 5 μm upon 515 nm excitation at various incident fluences, as indicated in the legend.(B) Fluence-dependent IR transient absorption pump-probe spectroscopy of a TiO2 sample.Ultrafast dynamics of TiO2 were probed at 5 μm upon 345 nm excitation at various incident fluences, as indicated in the legend.

Fig. S6 .
Fig. S6.(A) Electron-phonon relaxation times t e-ph extracted from fitting the transient absorption traces to the two-temperature model as a function of incident pump fluence for AuNRs (orange squares) and AuNRs@TiO 2 (blue squares) with 515 nm excitation.The probe wavelength was at the SPR maxima of 685 and 715 nm for the AuNR and AuNR@TiO2 samples, respectively.The lines are linear regressions of the data.(B) Electron-phonon relaxation times t e-ph extracted from fitting the transient absorption traces to the two-temperature model as a function of incident pump fluence forAuNRs (orange diamonds) and AuNRs@TiO 2 (blue diamonds) with 400 nm excitation.The probe wavelength was at the SPR maxima of 685 and 715 nm for the AuNR and AuNR@TiO2 samples, respectively.The lines are linear regressions of the data.TableS1lists the fitted slopes.

Fig. S7 .
Fig. S7.The integral J(w) for the TiO2 induced resonance state with width (FWHM) Λ = 0.8 eV.The dotted line represents the observed position (W =1.82 eV) of the AuNR SPR.

Fig. S8 .
Fig. S8.The integral Im  C () for the TiO2 induced resonance state with width (FWHM) Λ = 0.8 eV.The dotted line represents the observed position (W=1.82eV) of the AuNR SPR.

Fig. S9 .
Fig.S9.Effect of adsorbate resonance state and effective particle radius on CID.(A) Change in Γ >&Y as a function of the ratio of the absorbate resonance and the SPR.As the plasmon energy becomes larger than the adsorbate resonance energy, ( E −  A )/ Z-@ → 0, charge transfer is predicted to increase.Note that there is no hard cut-off for ( E −  A )/ Z-@ > 1 here because of the width Λ of the adsorbate state.(B) Change in Γ >&Y as a function of equivalent particle radius.Smaller particles are expected to have larger CID.

Table S1 .
Fitted slopes of pump power dependent measurements, forcing the intercept to be 0, as discussed in the main text and supplementary information.

Table S2 .
Tangential and normal contributions of TiO2 to the SPR width calculated using different values of  E (eV) at two different surface adsorbate concentrations.